Data-driven physics-informed neural networks for predicting coupled consolidation coefficients in two-dimensional soil systems

Two-dimensional soil consolidation involves coupled vertical and horizontal drainage, posing challenges in accurately predicting consolidation coefficients due to complex boundary conditions and data limitations in real-world applications. This study addresses these issues by evaluating data-driven physics-informed neural networks (PINNs) for solving forward and inverse problems in 2D consolidation with coupled consolidation coefficients. The methodology integrates hard constraints for drainage boundaries and soft constraints for both drainage and impermeable boundaries, enabling precise modelling of excess pore pressure and coefficient interactions. Forward problems were analysed with and without observed data, optimising hyperparameters and assessing sensor arrangement effects on predictions. Inverse problems utilised observed data to estimate vertical and horizontal consolidation coefficients and incorporated noise to simulate practical scenarios. Results show that PINNs accurately predict the full consolidation process, determining coefficients from initial-period data alone and robustly handling noise levels typical in field measurements. This work contributes a novel, efficient PINN-based approach for consolidation analysis with coupled coefficients, offering practical advantages for geotechnical engineering where long-term data is scarce and measurements are error-prone.